Arithmetic and Geometric Sequence and Series Flashcard

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What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. For example, 2, 4, 6, 8 is an arithmetic sequence with a common difference of 2.

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What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, 3, 6, 12, 24 is a geometric sequence with a common ratio of 2.

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How do you find the nth term of an arithmetic sequence?

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The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

How do you find the nth term of a geometric sequence?

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The nth term of a geometric sequence can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

What is the formula for the sum of the first n terms of an arithmetic series?

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The sum of the first n terms of an arithmetic series can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_1 is the first term and a_n is the nth term.

Front

What is the formula for the sum of the first n terms of a geometric series?

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The sum of the first n terms of a geometric series can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), where a_1 is the first term and r is the common ratio.

Front

What is an infinite geometric series?

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An infinite geometric series is the sum of the terms of a geometric sequence that continues indefinitely. It converges if the absolute value of the common ratio is less than 1.

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What is the sum of an infinite geometric series?

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The sum of an infinite geometric series can be calculated using the formula: S = a_1 / (1 - r), where a_1 is the first term and r is the common ratio, provided |r| < 1.

Front

What is the common difference in an arithmetic sequence?

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The common difference in an arithmetic sequence is the constant amount that each term increases or decreases by. It is calculated as d = a_n - a_(n-1).

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What is the common ratio in a geometric sequence?

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The common ratio in a geometric sequence is the factor by which each term is multiplied to get the next term. It is calculated as r = a_n / a_(n-1).